Bias by Necessity: Impossibility Theorems for Sequential Processing with Convergent AI and Human Validation
It provides a formal mathematical foundation for why certain cognitive biases are unavoidable in sequential processing systems, with implications for AI alignment and human decision-making.
The paper proves that cognitive biases like primacy effects and anchoring are mathematically inevitable in autoregressive language models due to causal masking, and validates these predictions across 12 LLMs and two human experiments (N=464), showing convergent evidence that biases are resource-rational responses to sequential processing.
Are certain cognitive biases mathematically inevitable consequences of sequential information processing? We prove that primacy effects, anchoring, and order-dependence are architecturally necessary in autoregressive language models due to causal masking constraints. Our three impossibility theorems establish: (1) primacy bias arises from asymmetric attention accumulation; (2) anchoring emerges from sequential conditioning with provable information bounds; and (3) exact debiasing by permutation marginalization requires factorial-time computation, with Monte Carlo approximation feasible at constant per-tolerance overhead. We validate these bounds across 12 frontier LLMs ($R^2 = 0.89$; $Δ$BIC $= 16.6$ vs. next-best alternative). We then derive quantitative predictions from the framework and test them in two pre-registered human experiments ($N = 464$ analyzed). Study 1 confirms anchor position modulates anchoring magnitude ($d = 0.52$, BF$_{10} = 847$). Study 2 shows working memory load amplifies primacy bias ($d = 0.41$, BF$_{10} = 156$), with WM capacity predicting bias reduction ($r = -.38$). These convergent findings reframe cognitive biases as resource-rational responses to sequential processing.